A Galois correspondence for II1 factors and quantum groupoids

Academic Article


  • We establish a Galois correspondence for finite quantum groupoid actions on II_1 factors and show that every finite index and finite depth subfactor is an intermediate subalgebra of a quantum groupoid crossed product. Moreover, any such a subfactor is completely and canonically determined by a quantum groupoid and its coideal *-subalgebra. This allows to express the bimodule category of a subfactor in terms of the representation category of a corresponding quantum groupoid and the principal graph as the Bratteli diagram of an inclusion of certain C^*-algebras related to it.
  • Authors

  • Nikshych, Dmitri
  • Vainerman, L
  • Status

    Publication Date

  • December 1, 2000
  • Has Subject Area

    Published In


  • math.OA
  • math.QA
  • Digital Object Identifier (doi)

    Start Page

  • 113
  • End Page

  • 142
  • Volume

  • 178
  • Issue

  • 1